binary / hex / decimal / octal

(for a preview of the online guide im working on, download in .odt here:  figguide0_2)

 

inside your computer are tons of tiny switches that let electricity through if theyre on, and dont if theyre off. together, they let the computer represent numbers.

when one of these switches is on, it represents 1. when its off, it represents 0.

usually we count based on 10, like 10 fingers. thats called “decimal.” if you can imagine the mile-counter inside a car, the numbers roll from 0… 1… 2, 3, 4, 5, 6, 7, 8, 9, then when it rolls back to 0 the next wheel over counts up: 1…

  • 0 0 0 “zero”
  • 0 0 1 “one”
  • 0 0 2 “two”
  • 0 0 3 “three”
  • 0 0 4 “four”
  • 0 0 5 “five”
  • 0 0 6 “six”
  • 0 0 7 “seven”
  • 0 0 8 “eight”
  • 0 0 9 “nine” (and next: roll over…)
  • 0 1 0 “ten”
  • and so on…

binary counts the same way, except each “wheel” would only have 0 and 1. so it rolls from 0 to 1… then when it rolls back to 0 the next wheel over counts up: 1… and so on.same rules, smaller wheels.

  • 0 0 0 “zero”
  • 0 0 1 “one” (and next: roll over first wheel…)
  • 0 1 0 “two”
  • 0 1 1 “three” (and next: roll over both wheels…)
  • 1 0 0 “four”
  • 1 0 1 “five”
  • and so on…

so thats how the computer stores numbers. but compared to decimal numbering, binary is tedious for most people. there are other numbering systems that make it easier to work with decimal and binary together. these include:

  • octal (just like binary goes from 0-to-1 instead of 0-to-9 before rolling over, octal goes from 0-7)
  • hexadecimal (6 plus 10, “hex” for short) goes 0… 1… 2, 3, 4, 5, 6, 7, 8, 9… a, b, c, d, e, f (really, it has 6 letters)

so if you see ff somewhere related to computers, it probably means 255 (in decimal.)

computers store all information as numbers. for example, a lower case a is usually stored as the number 97. the symbol for “nine”: 9 is represented like this in binary: 00111011 while the actual numeric value of 9 is 00001001.

when you drive your car down the road, the mile-counter doesnt know what a “mile” means to us as a concept, it just counts the number of times a wheel spins. the computer doesnt know the context of these numbers either– it simply does whatever its told to do with them.

the color black in hexadecimal is stored as 000000 or decimal: (0, 0, 0)… white is ffffffor decimal: (255, 255, 255). this system allows for the numbering of over 16 million values– you can add another number for how much you can “see through” the color (so you can draw things that mix, or overlap.)

“hello” in binary numbering is: 01101000 01100101 01101100 01101100 01101111 …but the spaces are only added here to make it “easier” for you to read. (a space is actually 00100000)

 

 

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